Periodic solutions for second order singular damped differential equations

We study the existence of positive periodic solutions for second order singular damped differential equations by combining the analysis of the sign of Green?s functions for the linear damped equation, together with a nonlinear alternative principle of Leray–Schauder. Recent results in the literature are generalized and significantly improved.     

Two-player simultaneous location game: Preferential rights and overbidding

Competitive location problems can be characterized by the fact that the decisions made by others will affect our own payoffs. In this paper, we address a discrete competitive location game in which two decision-makers have to decide simultaneously where to locate their services without knowing the decisions of one another. This problem arises in a franchising environment in which the decision-makers are the franchisees and the franchiser defines the potential sites for locating services and the rules of the game. At most one service can be located at each site, and one of the franchisees has preferential rights over the other. This means that if both franchisees are interested in opening the service in the same site, only the one that has preferential rights will open it. We consider that both franchisees have budget constraints, but the franchisee without preferential rights is allowed to show interest in more sites than the ones she can afford. We are interested in studying the influence of the existence of preferential rights and overbidding on the outcomes for both franchisees and franchiser. A model is presented and an algorithmic approach is developed for the calculation of Nash equilibria. Several computational experiments are defined and their results are analysed, showing that preferential rights give its holder a relative advantage over the other competitor. The possibility of overbidding seems to be advantageous for the franchiser, as well as the inclusion of some level of asymmetry between the two decision-makers.     

A New Ent-Kaurane from the Roots of Lasianthaea aurea

Chemistry of Natural Compounds - A known kaurenoic acid (1), together with a new kaurane derivative named 3α-isobutyryloxykaurenoic acid (2), was isolated from the roots of Lasianthaea aurea,...     

5‐Methyl‐N‐[2‐nitro‐4‐(trifluoromethyl)phenyl]‐1H‐pyrazole‐3‐amine: a chain of hydrogen‐bonded R22(6) and R22(16) rings

The molecular skeleton of the title compound, C₁₁H₉F₃N₄O₂, is almost planar and exhibits a polarized (charge‐separated) electronic structure in the nitroaniline portion. Molecules are linked by N—H...N and C—H...O hydrogen bonds to form a chain in which centrosymmetric R₂²(6) and R₂²(16) rings alternate.     

Thermogravimetric studies on catalytic effect of metal oxide nanoparticles on asphaltene pyrolysis under inert conditions

This study investigated the catalytic effect of NiO, Co₃O₄ and Fe₃O₄ nanoparticles toward asphaltene thermal decomposition (pyrolysis) under inert conditions. Asphaltene adsorbed onto the selected nanoparticles were subjected to thermal decomposition up to 800?°C in a thermogravimetric analyzer. The presence of nanoparticles caused a significant decrease in the asphaltene decomposition temperature and activation energy. Activation energies for the process were calculated using the Ozawa?CFlynn?CWall method. All the selected metal oxide nanoparticles showed high catalytic activity toward asphaltene decomposition in the following order NiO?>?Co₃O₄?>?Fe₃O₄. This study confirms that metal oxide nanoparticles can significantly enhance the thermal decomposition of heavy hydrocarbons, like asphaltenes.